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Abstract

A novel transient thermal characterization technology is developed based on the principles of transient optical heating and Raman probing: time-domain differential Raman. It employs a square-wave modulated laser of varying duty cycle to realize controlled heating and transient thermal probing. Very well defined extension of the heating time in each measurement changes the temperature evolution profile and the probed temperature field at μs resolution. Using this new technique, the transient thermal response of a tipless Si cantilever is investigated along the length direction. A physical model is developed to reconstruct the Raman spectrum considering the temperature evolution, while taking into account the temperature dependence of the Raman emission. By fitting the variation of the normalized Raman peak intensity, wavenumber, and peak area against the heating time, the thermal diffusivity is determined as 9.17 × 10−5, 8.14 × 10−5, and 9.51 × 10−5 m2/s. These results agree well with the reference value of 8.66 × 10−5 m2/s considering the 10% fitting uncertainty. The time-domain differential Raman provides a novel way to introduce transient thermal excitation of materials, probe the thermal response, and measure the thermal diffusivity, all with high accuracy.

Figures (6)

(a) Timing profiles of the laser pulse and the temperature evolution, and instant changes of Raman peak intensity (I), peak shift (ω) and linewidth (Γ). Along with the heating, the temperature in the sample increases, and then the Raman peak intensity decreases, the wavenumber softens and linewidth broadens. In TD Raman, the laser heating time is increased a little bit (Δte) each time from Case 1 to Case 3. Therefore, the temperature of the heated region will experience more increase (before reaching the steady state) from Case 1 to Case 3. This extended temperature rise will give rise to a slight change in the Raman spectrum collected during the heating period. (b) The corresponding temporally accumulative Raman spectra of one cycle in three cases. Slight Raman peak softening due to the increased differential heating time is marked in the figure. The peak intensity increases largely because of the longer excitation period. The heating induced intensity decrease is less obvious in these spectra, but is visible via further peak analysis.

(a) The optical microscope view of the tipless Si cantilever. It is 450.35 μm long and 49 μm wide. The tip has a height of 22.95 μm. (b) Schematic of laser spot position on the cantilever tip end. The effective heating region is marked with x1 and x2 on the x coordinate in the physical model. le ( = x2 - x1) is 19.9 μm indicating the effective length of the heating region on the cantilever. L is the total effective length (438.9 μm) used for the cantilever in the physical model.

The evolution of the Si Raman peak against the increase of excitation/heating duty in the experiment. (a) Spectra per cycle under different excitation time of te: 0.24 ms, 0.4 ms, 0.68 ms, 1.16 ms, 1.72 ms, 4.2 ms, and 10 ms. As the excitation/heating time becomes longer, the Raman peak in one cycle increases and softens to the left. (b) Raman emission Eω ( to the left y axis) increase against te, but the rate ∂Eω/∂tedeclines quickly at the beginning and then slows down to a constant. The normalized Raman emission Eω* ( to the right y axis) decreases to a steady state value as te become longer. Eω* directly illustrates that the Raman emission per unit time decreases against the heating time. (c) Raman linewidth variation against the excitation time. Although an increasing trend is observed for the linewidth against increased excitation time, large noises are observed in linewidth data due to the less sensivity of linewidth to temperature variation. So this data is less applicable for thermal diffusivity determination. (d) A clear decline in the wavenumber against te makes wavenumber ω a good property for detemining α of the cantilever.

(a) The evolution of the reconstructed Si Raman spectrum per cycle with the numerical method against the increase of Fourier number Foe (te): 0.028, 0.047, 0.079, 0.14, 0.20, 0.49, and 1.17. The Raman peak in one cycle increases and softens to the left against the increased Foe. This echoes the one in Fig. 3(a). (b) The decreasing trends of the normalized Raman intensity Eω* and (c) the Raman shift ω against the Fourier number Foe well agree with the trends in the experiment.

(a) Variation of normalized intensity against the excitation time. It decreases as te is increasing to a steady state value. The red curve with αEω* of 9.17 × 10−5 m2/s best fits the experimental data based on the intensity method. (b) Wavenumber shift to the steady state against the excitation time. The best fitted curve with αω of 8.14 × 10−5 m2/s is shown red. Error bars in both figures show the uncertainty in the measurement, and curves with 10% deviation in both thermal diffusivities are shown in blue and green. They show obvious difference from the best fitted results indicating the sensitivity of the normalized Raman intensity method and wavenumber shift method, respectively.

The experimental data fitting based on the peak area with the best fitted curve with αE* = 9.51 × 10−5 m2/s. The measurement uncertainty is shown using error bars. The sensitivity of the total Raman emission method to α is shown with α = 8.56 × 10−5 m2/s and α = 10.47 × 10−5 m2/s, respectively. A visible deviation is observed from the best fitted result when α changes with 10%.